Exact uniform modulus of continuity for $q$-isotropic Gaussian random fields

TL;DR

This paper establishes precise conditions under which $q$-isotropic Gaussian random fields exhibit an exact uniform modulus of continuity, with applications to multidimensional $B^{eta}$ Gaussian processes.

Contribution

It provides the first exact uniform modulus of continuity results for $q$-isotropic Gaussian fields and extends these results to multidimensional $B^{eta}$ processes.

Findings

Derived sufficient conditions for exact uniform modulus continuity.

Applied the results to multidimensional $B^{eta}$ Gaussian processes.

Enhanced understanding of regularity properties of $q$-isotropic Gaussian fields.

Abstract

We find sufficient conditions for the existence of an exact uniform modulus continuity for the class of $q$-isotropic Gaussian random fields introduced in [8]. We apply the result to a $d$-dimensional version of the $B^{\gamma}$ Gaussian processes defined in [14].